Abstract

We present a family of asymmetric phase masks that extends the depth of field of an optical system. To verify our proposal, we compute several modulation transfer functions with focus errors, and we report numerical simulations of the images that can be achieved by use of our proposed procedure.

© 2004 Optical Society of America

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References

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  1. M. Mino, Y. Okano, “Improvement in the OTF of a defocused optical system through the use of shade apertures,” Appl. Opt. 10, 2219–2224 (1971).
    [CrossRef] [PubMed]
  2. Gerd Häusler , “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
  3. J. Ojeda-Castañeda, P. Andrés, A. Díaz, “Annular apodizers for low sensitivity to defocus and to spherical aberration,” Opt. Lett. 11, 487–489 (1986).
    [CrossRef] [PubMed]
  4. J. Ojeda-Castañeda, L. R. Berriel-Valdos, E. Montes, “Bessel annular apodizers: imaging characteristics,” Appl. Opt. 26, 2770–2772 (1987).
    [CrossRef] [PubMed]
  5. J. Ojeda-Castañeda, L. R. Berriel-Valdos, “Arbitrarily high focal depth with finite apertures,” Opt. Lett. 13, 183–185 (1988).
    [CrossRef] [PubMed]
  6. J. Ojeda-Castañeda, A. Noyola-Isgleas, “High focal depth by apodization and digital restoration,” Appl. Opt. 27, 2583–2586 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. J. Ojeda-Castañeda, A. Castro, J. Santamaría, “Phase mask for high focal depth,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 14 (1999).
    [CrossRef]
  9. E. R. Dowski, G. E. Johnson, “Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fisher, W. J. Smith, eds., Proc. SPIE3779, 137–145 (1999).
    [CrossRef]
  10. S. Mezouari, A. A. Harvey, “Phase pupil functions reduction of defocus and spherical aberrations,” Opt. Lett. 28, 771–773 (2003).
    [CrossRef] [PubMed]
  11. K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
    [CrossRef]
  12. J. Ojeda-Castañeda, L. R. Berriel-Valdos, “Ambiguity function as a design tool for high focal depth,” Appl. Opt. 27, 790–795 (1988).
    [CrossRef] [PubMed]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), pp. 148–151.
  14. J. Ojeda-Castañeda, A. Castro, “Simultaneous Cartesian coordinate display of defocused optical transfer functions,” Opt. Lett. 23, 1049–1051 (1998).
    [CrossRef]
  15. H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, Oxford, 1950), pp. 48–55.
  16. P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, Oxford, 1997), pp. 206–212.
  17. J. H. McLeod, “The Axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  18. A. W. Lohmann, “Lente focale variabile,” Italian patent727,848 (19June1964).
  19. A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. 9, 1669–1671 (1970).
    [CrossRef] [PubMed]
  20. L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent3,305,294 (3December1964).
  21. K. R. Castleman, Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1996), pp. 387–403.
  22. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 268–290.

2003 (1)

1998 (1)

1995 (1)

1988 (3)

1987 (1)

1986 (1)

1983 (1)

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

1972 (1)

Gerd Häusler , “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).

1971 (1)

1970 (1)

1954 (1)

Alvarez, L. W.

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent3,305,294 (3December1964).

Andrés, P.

Berriel-Valdos, L. R.

Brenner, K. H.

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1996), pp. 387–403.

Castro, A.

J. Ojeda-Castañeda, A. Castro, “Simultaneous Cartesian coordinate display of defocused optical transfer functions,” Opt. Lett. 23, 1049–1051 (1998).
[CrossRef]

J. Ojeda-Castañeda, A. Castro, J. Santamaría, “Phase mask for high focal depth,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 14 (1999).
[CrossRef]

Cathey, W. T.

Díaz, A.

Dowski, E. R.

E. R. Dowski, W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1865 (1995).
[CrossRef] [PubMed]

E. R. Dowski, G. E. Johnson, “Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fisher, W. J. Smith, eds., Proc. SPIE3779, 137–145 (1999).
[CrossRef]

Gerd Häusler,

Gerd Häusler , “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 268–290.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), pp. 148–151.

Harvey, A. A.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, Oxford, 1950), pp. 48–55.

Johnson, G. E.

E. R. Dowski, G. E. Johnson, “Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fisher, W. J. Smith, eds., Proc. SPIE3779, 137–145 (1999).
[CrossRef]

Lohmann, A. W.

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

A. W. Lohmann, “A new class of varifocal lenses,” Appl. Opt. 9, 1669–1671 (1970).
[CrossRef] [PubMed]

A. W. Lohmann, “Lente focale variabile,” Italian patent727,848 (19June1964).

Macdonald, J.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, Oxford, 1997), pp. 206–212.

McLeod, J. H.

Mezouari, S.

Mino, M.

Montes, E.

Mouroulis, P.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, Oxford, 1997), pp. 206–212.

Noyola-Isgleas, A.

Ojeda-Castañeda, J.

Okano, Y.

Santamaría, J.

J. Ojeda-Castañeda, A. Castro, J. Santamaría, “Phase mask for high focal depth,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 14 (1999).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 268–290.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

K. H. Brenner, A. W. Lohmann, J. Ojeda-Castañeda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44, 323–326 (1983).
[CrossRef]

Gerd Häusler , “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).

Opt. Lett. (4)

Other (9)

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, Oxford, 1950), pp. 48–55.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, Oxford, 1997), pp. 206–212.

A. W. Lohmann, “Lente focale variabile,” Italian patent727,848 (19June1964).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996), pp. 148–151.

J. Ojeda-Castañeda, A. Castro, J. Santamaría, “Phase mask for high focal depth,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 14 (1999).
[CrossRef]

E. R. Dowski, G. E. Johnson, “Wavefront coding: a modern method of achieving high-performance and/or low-cost imaging systems,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fisher, W. J. Smith, eds., Proc. SPIE3779, 137–145 (1999).
[CrossRef]

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent3,305,294 (3December1964).

K. R. Castleman, Digital Image Processing (Prentice Hall, Englewood Cliffs, N.J., 1996), pp. 387–403.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 268–290.

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Figures (9)

Fig. 1
Fig. 1

Schematic of a 1-D optical system for extending the depth of field: (a) layout and (b) lens arrangement.

Fig. 2
Fig. 2

(a) Ambiguity function and (b) defocused MTFs for the asymmetric phase profile in Eq. (7).

Fig. 3
Fig. 3

Asymmetric phase profiles of the order n = 3, 4, 5, and 6 versus the normalized spatial frequency.

Fig. 4
Fig. 4

(a) Ambiguity function and (b) defocused MTFs for the asymmetric phase profile of the order n = 4.

Fig. 5
Fig. 5

Same as Fig. 4, but for the asymmetric phase profile of the order n = 5.

Fig. 6
Fig. 6

Same as Fig. 5, but for the asymmetric phase profile of the order n = 6.

Fig. 7
Fig. 7

Comparison between the MTFs, with focus error of one wavelength, for the asymmetric phase-profile orders of (a) n = 3, 4, 5, and 6 and (b) n = 7, 8, 9, and 10.

Fig. 8
Fig. 8

Numerical simulations of a spoke pattern. The first row is the clear aperture.

Fig. 9
Fig. 9

Same as Fig. 8, but for the order n = 7, 8, 9, 10, and 12.

Tables (1)

Tables Icon

Table 1 Classification Scheme for Visualizing the Asymmetric Phase Family in the Context of Other Phase Profiles

Equations (12)

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f1r=rf, f2s=f/s,
F1r=rr+1 f,
F2s=1s+1 f.
Z1r=-rf, Z2s=-f/s,
Pμ=expi2παμ/Ω2Qμ.
Qμ=1 if |μ|Ω=0 if |μ|>Ω.
Pμ=expi2παsgnμμ/Ω2Qμ.
sgnμ=1 if μ>0=-1 if μ<0.
Pμ=expi2παsgnμμ/ΩnQμ.
Hμ; W20= Pν+μ/2P*ν-μ/2expi2π2W20λΩ2 μνdν,
Aμ, y= Pν+μ/2P*ν-μ/2expi2πyνdν,
Hμ; W20=Aμ, y=2W20λΩ2 μ.

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